Pipe Volume Calculator

Enter the outer radius, inner radius and length of a pipe — a hollow cylinder — for the volume of wall material, the curved surface areas and the wall thickness, drawn to scale. Click any amber dimension on the drawing to change it. For the flat ring on its own, see the annulus calculator.

Dimensions

Pipe
Blueprint · Isometric Click an amber dimension to edit it · isometric, not to printed scale

Result

Volume of a pipe

A pipe is a cylinder with a cylinder removed: the material left is the outer cylinder's volume minus the bore's, V = πR²h − πr²h. Its cross-section is an annulus — a flat ring — with area π(R² − r²).

Bore or capacity?

This tool gives the volume of the wall material. If you want how much the pipe carries, that is the bore: a plain cylinder of radius r, which the cylinder calculator handles.

How to find the volume of a pipe

A pipe, tube or sleeve is a hollow cylinder: an outer cylinder of radius R with a bore of radius r removed. Two questions come up and they have different answers. How much material is in the wall? That is this calculator. How much does the pipe carry? That is the bore — an ordinary cylinder of radius r.

The formula

The wall volume is the difference of the two cylinders, which factors neatly through the ring-shaped cross-section:

V = πh(R² − r²)
A = 2πh(R + r) + 2π(R² − r²)
wall = R − r

Worked example

Take a pipe with outer radius 40, inner radius 26 and length 90.

Step 1 — ring cross-section

The area of the annular cross-section.

π(40² − 26²) = π(1,600 − 676) = 924π ≈ 2,902.83
Step 2 — volume

Cross-section times length.

V = 924π × 90 = 83,160π ≈ 261,254.72
Step 3 — wall thickness

Outer radius minus inner radius.

40 − 26 = 14

What else the calculator returns

You get the outer curved surface (2πRh), the inner curved surface lining the bore (2πrh), the two flat ring ends together, the total of all four, and the wall thickness. Everything updates as you edit the figure, and the drawing shows the wall honestly — a thin-walled tube and a thick sleeve look genuinely different.

Where it comes up

Pipe weight is wall volume times material density, so this is the calculation behind steel and PVC pipe weight tables, hollow shafts and axles, sleeves and bushings, structural hollow sections, conduit, and the concrete in a cored column. The flat-ring version of the same shape — washers, gaskets, running tracks — is the annulus calculator.

Frequently asked questions

How do you find the volume of a pipe?

Subtract the bore from the outer cylinder: V = πR²h − πr²h = πh(R² − r²), where R is the outer radius, r the inner radius and h the length.

Is this the volume of material or what the pipe holds?

Material. The wall volume is πh(R² − r²). What the pipe holds is the bore, a plain cylinder: πr²h.

I have diameters and a wall thickness — how do I convert?

Halve each diameter to get a radius. From an outer diameter D and wall t, the inner radius is D⁄2 − t. You can also click the ⌀ values on the drawing and type diameters directly.

How do I work out the weight of a pipe?

Multiply the wall volume by the material density in matching units. In millimetres, V × 7.85×10⁻⁶ gives kilograms for steel (7.85 g/cm³).

What shape is the cross-section of a pipe?

An annulus — the flat ring between two concentric circles, with area π(R² − r²). The annulus calculator covers it in 2D.